AO Maps, Directed AO Maps and Cavity Maps, Oh My!
Your question is really multiple questing so should probably be split up, but I'll answer what I can anyway.

Ambient Occlusion is mostly a hangover for old rendering methods where there was a a global 'ambient' light/colour which was used to brighten the scene in lieu of more proper global illumination techniques such as pathtracing (see https://en.wikipedia.org/wiki/Shading#Ambient_lighting). This ambient lighting method is used by blender render for example. Ambient occlusion is a way of improving on this by re-introducing dark shadows in cavities. Because of this, unless you are using a very low number of bounces, this should not be necessary at all in cycles. If you do need to, ambient occlusion maps are usually used to multiply the diffuse texture (often this is actually merged into the one texture).

parallax mapping is just an advanced form of bump mapping which accounts for view angle and is really for realtime engines. When rendering with cycles you are better of just trying proper displacement mapping either through the modifier or the experimental rendertime feature

In my understanding, cavity maps are just textures that allow you to distinguish cavities in your model, they can be calculated in any number of ways. I imagine various software calculates them differently, and ambient occlusion maps can certainly be used as cavity maps. They are largely used for masking and effects in various texturing tools.

I haven heard of directed AO maps, but your article suggests that the directed part comes from the light source, so this would easily be doable the same way as a normal AO map assuming that the light and the object the map is for are both static. I guess it might be possible to do something clever with normal + light direction to control the strength of normal AO to get a similar effect.